Download Perfectly inelastic collision

One Dimension: Conservation of
Linear Momentum
Misaki, Christine, and Bonny
Elastic Collisions
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•
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Elastic collisions: objects do NOT stick together after collision (the two general cases are
shown below)
Momentum conserved
m1vi + m2vi = m1vf + m2vf
Kinetic energy conversed
½ m1vi + ½ m2vi = ½ m1vf + ½m2vf
Only under certain conditions:
–
–
Force of friction is negligible
Energy is not lost in the form of sound or heat
If two objects have the SAME
mass, all of the KE will be
transferred to the other
(assuming that the second
object was initially at rest):
If the two objects have
DIFFERENT masses, a
collision like this may happen:
Inelastic Collision
• Perfectly inelastic collision: colliding objects
stick together after the collision
– In reality, everything is NOT perfectly inelastic, but in
physics problems done in class at this level, inelastic
collisions implies that it is perfectly inelastic.
• Momentum conserved
m1vi + m2vi = MV and M = m1 + m2
• Kinetic energy NOT conserved
Unlike elastic
collisions, inelastic
collisions can happen
regardless of the two
objects mass:
+ and Hovercraft 1
Hovercraft 2
Notes on using LoggerPro:
•Set origin (you can tilt the origin to
fit your situation using the yellow dot
on the right hand side as shown
above)
•Use a meter stick or some sort of
reference point for distance
• LoggerPro only allows the user
to set ONE origin (shown with
the yellow intersecting lines)
• Hovercraft 1’s initial position
will be x = 0 (at the origin)
• Hovercraft 2’s initial position
will be x = some negative
number b/c it will be the
displacement relative to origin
– As it moves towards HC1, the
HC2’s position will become less
negative (the number will
increase)
• This will also explain why the
velocities of the two HCs are
negative.
Demonstration of 1D Collision
• B/c this demonstration was not done in
ideal situations, there is a force of friction
between the Hovercrafts and the floor.
• Although very small, there is some air
resistance as well.
• In real situations, it is very hard to observe
the conservation of linear momentum.
Often, some of the KE will be lost.
Position vs. Time Graphs of Both Hovercrafts
Graphs will be explained in detail in the following slides!
Hovercraft 1: Position vs. Time
• Slope of the best fit line is
the velocity of HC1
• Negative value b/c the
origin was set on the right
and the object was moving
away from the origin
towards the left
• Approximately at t=7.4,
the velocity of hovercraft 1
becomes zero b/c all
kinetic energy passed onto
hovercraft 2 since they
have the same mass.
Hovercraft 2: Position vs. Time
• Slope of the best fit line
is velocity (v= .4755m/s)
– It is NOT perfectly linear
b/c some errors were
made when plotting the
points with LoggerPro
(human error).
• Velocity of HC is zero
from t=0 to t=7.4 b/c the
HC2 was at rest until
HC1 hit HC2 at
immediately after t=7.4
Hovercraft 1: Velocity vs. Time
LoggerPro Notes
These adjustments need to be made b/c of
how the origin was set in this program.
•Negative acceleration values = HC is
accelerating
•Positive acceleration values = HC is
decelerating
• Slopes of best fit lines
are the acceleration.
• Initially, the HC
accelerates at the value
of a=9.7 m/s2 due to the
force exerted on it by the
initial push.
• Then, the HC starts to
decelerate b/c of the
force of friction that
overcomes the initial
force provided by the
push.
Hovercraft 2: Velocity vs. Time
• Slopes of best fit lines
are the acceleration.
• Initially, the HC
accelerates at the value
of a=9.7 m/s2 due to the
force exerted on it by
HC1.
• Then, the HC2 starts to
decelerate b/c of the
force of friction that
overcomes the initial
force provided by the
push.
Conservation of
Momentum
Pinitial = Pfinal
m1vi + m2vi = m1vf + m2vf
m1=m2
m1vi + m2vi = m1vf + m2vf
.8210 + 0 ≈ 0 + .6961
.8210 ≈ .6961
Loss of kinetic energy can be accounted for
by the effects of the external forces.
Results also follow a logical pattern:
Hovercraft 1 has a higher velocity than
the resulting velocity of Hovercraft 2.
Some of the energy could have been
translated into heat or sound at the time
of the collision.
**Human error when plotting the points also
explain why the two numbers are not
perfectly equal to each other.